1. The problem statement, all variables and given/known data Give an example of a cubic polynomial, defined on the open interval (-1,4), which reaches both its maximum and minimum values. 2. Relevant equations - 3. The attempt at a solution I can see that I would need a function such that there is some f(a) and f(b) in (f(-1),f(4)) such that f(a) >= all f(x) for x in (-1,4) and f(b) <= all f(x) for x in (-1,4). I used an online tool to adjust the coefficients of a cubic until I got what I needed. But I have no idea how to do this by myself. All that I can think of is to somehow use the fact that at extrema, a function's derivative is zero.